Introduction
Wavelet analysis (WA) is a perspective method for performing spectral analysis of laser Doppler (LD) microcirculatory signals. WA decomposes LD signals into wavelet spectra consisting of six frequency intervals related to physiological influences (endothelial nitric oxide (NO)-independent, endothelial NO-dependent, neurogenic, myogenic, respiratory, and cardiac) that modulate the microcirculatory response and range from 0.005-2 Hz [1].
As WA is applied to finite length signals, the analysis results inevitably suffer from edge effects that lead to distortions of the spectral amplitude. The cone of influence (COI), defined as the e-folding time for the autocorrelation of wavelet transform at each scale, delineates the regions of the wavelet spectrum where such edge effects become important [2,3]. Since the cone of influence reduces the available data, these regions can affect the relevance of the results provided [4]. However, the extent to which performing WA by considering the values outside the COI affects the analysis results has not yet been fully investigated.
Aims
We aimed to determine whether accounting for COI leads to significant differences in the results obtained by WA. We observed two typical patterns of LD signal: a stationary signal represented by the baseline LD signal and a complex transient signal represented by the post-occlusive phase of transient arterial occlusion.
Method
Following ethical approval by the National Ethics Committee of the Republic of Slovenia (no. 87/06/13), eighteen healthy young volunteers were recruited.
LD signals were acquired at the volar forearm during a five-minute baseline recording, a transient three-minute occlusion of the brachial artery, and a recovery phase lasting an additional five minutes.
WA was performed on the signals acquired during the baseline and recovery phases. The time-averaged wavelet spectra were constructed in two ways: with and without the data affected by edge effects (i.e. without and with COI correction).
To compare the contribution of different physiological mechanisms to the regulation of microcirculatory responses during these phases, the relative power (RP = median power of each frequency interval / median power of the total spectrum) was determined for each frequency interval of the corresponding phase.
A non-parametric Wilcoxon signed-rank test was used to compare the differences between the RP of the spectral components obtained without and with COI correction, respectively. The results are presented as group medians and the interquartile range.
Results
No statistically significant differences were found between the RPs of the baseline phase determined without and with COI correction. Statistically significant differences were observed in the RPs of the frequency bands associated with endothelial NO-independent (9.72 [6.76-11.76] without vs. 2.47 [1.27-4.44] with correction, p<0.001), endothelial NO-dependent (4.33 [2.58-7.61] without vs. 1.15 [0.76-2.47] with correction, p<0.001), neurogenic (1.89 [1.25-2.62] without vs. 1.12 [0.81-1.19] with correction, p<0.05), myogenic (0.84 [0.51-0.93] without vs. 1.06 [0.97-1.41] with correction, p<0.001), respiratory (0.33 [0.22-0.42] without vs. 0.51 [0.44-0.77] with correction, p<0.001) and cardiac (0.25 [0.16-0.59] without vs. 0.54 [0.31-0.95] with correction, p<0.001) influence.
Conclusion
Our results suggest that it may be crucial to adjust WA results for COI correction in case of transient LD signals, especially for low-frequency endothelial intervals that are questionable to evaluate in practice.