Heart Rate Variability in preterm neonates with and without abnormal cardiorespiratory events
Remark: research based on data and paper of Geert Morren
Data
Set of RR signals, measured on 34 neonates, divided in 4 groups:
- NN: normal PS + normal FU (10)
- AN: abnormal PS + normal FU (10)
- AA: abnormal PS + abnormal FU (10)
- Mille: normal PS + abnormal FU ?? (4) PS = polysomnography
FU = follow-up
Technique
A nonlinear data analysis technique is used: numerical noise titration. In fact, it is a better alternative for the Lyapunov exponent (LE), which is a measure of the exponential divergence of nearby states. LE fails to specifically distinguish chaos from noise and can not detect chaos reliably unless the data series are inordinately lengthy and virtually free of noise, but those requirements are difficult – mostly even impossible – to fulfill for most empirical data. In contrast, numerical noise titration is an analytical technique that provides a sufficient and robust numerical test of chaos and a relative measure of chaotic intensity, even in the presence of significant noise contamination.
White (or linearly correlated) noise of increasing standard deviation (σ) is added to data until its nonlinearity goes undetected (of course within a prescribed level of statistical confidence) by a particular indicator at a limiting value of σ = Noise Limit (NL value).
NL > 0 indicates chaos and the value of NL gives an estimate of its relative intensity.
Conversely, if NL = 0, then it may be inferred that the series either is not chaotic or the chaotic component is already neutralized by the background noise in the data) the so called “noise floor”). Therefore, the condition NL > 0 provides a simple sufficient test for chaos.
The indicator for the numerical titration of chaos with random noise could be – in theory – any noise-tolerant technique that can reliably detect nonlinear dynamics in short noisy series. Here, the Volterra-Wiener nonlinear identification method is used.
Numerical noise titration technique of C.S. Poon applied on RR interval series after resampling the signal to a constant sampling frequency of 2 Hz
- complete signal : mean duration of 8 hours (~ 75000 RR intervals) - QS1: first period of quiet sleep
- AS1: first period of active sleep
- QS: concatenation of all quiet sleep periods in complete signal - AS: concatenation of all active sleep periods in complete signal Cfr. Attach: list of all neonates with duration of complete signal, QS and AS
Measure
5 different parameters that can be used as feature to distinguish groups from each other (NN vs AN vs AA vs mille) or to distinguish periods of active sleep from periods of quiet sleep
- Mean: mean value of NL over all windows - Median: median value of NL over all windows
- Thresh1: relative number (in %) of NL values under 1%
- Thresh5: relative number (in %) of NL values under 5%
- Thresh10: relative number (in %) of NL values under 10%
Statistics
Statistical analysis is used to examine significant differences A. between groups
- student’s t-test, two sided, unpaired (two-sample, unequal variance) - Man-Whitney U test = Wilcoxon rank sum test
B. within each/all groups
- student’s t-test, two sided, paired - Wilcoxon signed rank test
The student’s t-test is a parametric test (cfr one-way ANOVA). This implicates that some assumptions are made that have to be satisfied before the results of the test can be
interpreted, namely the data (in this case one of the five parameters) must have a normal distribution.
On the other hand, the Wilcoxon rank sum test or the Wilcoxon signed rank test are nonparametric tests and do not require such assumptions.
In case of normal distributed data, a parametric test gives better (more accurate) results than a nonparametric test.
Take also into account that the groups are small.
Results
A. Between groups : mutual comparison between groups NN, AN, AA and mille
a) Complete signal
- no significant differences between groups, except for measures Thresh1 and Thresh5
- conclusion : low thresholds have a distinctive capacity which other measures such as mean or median do not have, particularly to
distinguish normal and abnormal PS b) QS1 period and QS periods
- remark first of all the lower values of NL (and so also mean NL or median NL), so there is less chaos in the segments of quiet sleep stage.
Often NL = 0 over whole segment (see table of results for QS1)
mean NL = 0 in 77% (24/34) of neonates during QS1
especially for groups NN and AA, so groups with an abnormal PS, which we could expect
- during QS1:
mean and median have distinctive character: NN vs.
AN, NN vs. AA
thresholding measures less powerfull and
significance depends on threshold value, but low thresholds seem to be a bit more accurate
- during QS in general:
significant differences over all measures: mille vs.
NN/AN/AA
clear difference between NN vs. AN, NN vs.
AA(cfr QS1), but not significant at 5% level and Wilcoxon rank sum test, while student’s t test gives more significant differences between these groups
- conclusion :
lower NL values during periods of quiet sleep in general (see within groups later)
despite significance for NN vs. AN and NN vs. AA during QS1, it is gone when considering all QS periods, although there still seems to be a difference. Suggestion: more data necessary
c) AS1 period and AS periods
- Sometimes high, sometimes extremely low (=0) NL values, depending on neonate, even within groups (NN, AN)
Difficult tot take conclusions
- during AS1:
mean and median have no distinctive character
thresholding measures give significant difference:
AA vs. mille
- during AS in general:
only significant difference for NN vs. AA, but even not for all measures
- conclusion :
no resemblance between AS1 and the more general
AS
diverse NL values: difficult to find some “rule”
Remark: QS1 and AS1 are (very) short periods, so not always representative due to restricted number of windows.
General conclusion between groups
In general, during periods of quiet sleep, the NL values (as result of the noise titration technique) are lower. This can be seen at first sight for all groups, except mille.
No ‘general rules’ concerning complete signal or
AS1/AS
Different conclusions for QS1 and the global QS.
Despite significance for NN vs. AN and NN vs. AA during QS1, it is gone when considering all QS periods, although there still seems to be a difference. Maybe more data is necessary to get again significance between these groups at the general level of all QS periods. New significances concerning the mille group during QS.
B. Within groups : mutual comparison between complete signal, QS(1) and AS(1)
a) NN
- Significant difference between complete signal and QS1 period, but only visible for mean as measure (p=0.005), not for other measures - Considering all periods (so QS and AS), it is very clear that
QS can be distinguished from AS or from the complete signal, and with all measures
- conclusion : strong significance for: complete vs. QS and QS vs. AS
b) AN
- QS1: NL = 0 over whole period and for each neonate in this group. Of course QS1 can be easily distinguished from the complete signal in a very significant way for all measures
- also significant difference for QS1 vs. AS1, but only with thresh-measures
- strong significance with all measures for: complete vs. QS and QS vs. AS
- conclusion : strong significance for: complete vs. QS and QS vs. AS
c) AA
- Clearly low NL values (less chaotic signals -> logic because abnormal) in QS1 and AS1 referred to complete signal, but this trend is mainly gone in AS periods and also less clear in QS periods (but still present) - Significance with all measures, except median: complete vs.
QS1, complete vs. AS1
- Significance with all measures, except median: complete vs.
QS, complete vs. AS and QS vs. AS
- conclusion : significance everywhere: complete vs. QS, complete vs. AS and QS vs. AS
d) mille
- while NL values seems to be lower during QS1, it is rather the opposite way when generalizing the first quiet sleep period to all quiet sleep periods
- no significance for QS1 or AS1
- significance between complete and QS, except for median measure
- conclusion : weak significance for complete vs. QS General conclusion within groups
In general, during periods of quiet sleep, the NL values (as result of the noise titration technique) are lower. This can be seen at first sight for all groups, except mille.
In almost each group, one remarks the same
conclusions, namely (strong) significance for complete vs. QS and QS vs. AS (even between complete and AS in AA group)
These general conclusions are confirmed when we make a comparison within all groups together, so taking 34 datasets together and make a paired comparison. Then there is a very strong significance (p=1E-5 or less) – even for all 5 measures – for complete vs. QS and QS vs. AS and for some measures even complete vs. AS
Influence of sampling frequency
Numerical noise titration technique is applied on RR interval series. In literature, one find that not always the original RR signal (directly extracted from the ECG measuring) is used, but one resamples this signal to a constant sampling frequency Fs.
In all results as described before, a sampling frequency of 2 Hz is chosen. In earlier published (conference) papers about this noise titration technique, the used Hs is not mentioned. Frank Beckers - of the unit Experimental Cardiology in UZ Gasthuisberg – told me that they resampled RR signals (if they do) to 2 Hz for persons, 10 Hz for rats (because heart rate is 5 times higher). Despite the higher heart rate, I also chose 2 Hz as Fs for the data of preterm neonates.
But, the chosen Fs can have an influence, and to study this, different values for Fs are tried out. The 10 datasets of the NN group are processed with the numerical noise titration technique after resampling the signal to different Fs, namely Fs = 2 Hz, 4 Hz, 6 Hz, 8 Hz, 10 Hz and 20 Hz.
The results for Fs = 2 Hz are very similar with the results by applying the technique to the original signal. This can be seen in different ways: same NL graph during time, nearly the same values for the 5 different measures.
The general observation concerning the sampling frequency to which the RR signal is resampled, is that the NL values decrease as Fs increase. Not only the plots of NL versus time for different Fs values show that, but also the tables with the results. Globally (for a certain neonate), the mean NL and the median NL becomes smaller and the thresholding measures larger when Fs is growing. An exception is Fs = 6 Hz, because the NL values are higher than those of Fs = 4Hz. No idea at this moment what the reason could be herefore.
Looking to the plots of NL versus time for different Fs values, it seems that in some specific regions, the chaos intensity seriously decrease as Fs increase. Why that region and not an other, is difficult to study. Is there some relationship with quiet or active sleep
periodes? Not at first sight. The higher Fs, the larger those regions are. For Fs = 10 or 20 Hz, NL becomes 0 over nearly the complete signal.
Conclusion
In general, NL values decrease as Fs increase (except Fs = 6Hz why ? )
What is the best sampling frequency? Discussion
necessary.
