302
M. Thanaj et al.
However, entropy measures do not show the same changes through scales as
complexity. Humeau et al. [41] in a recent study of the multiscale entropy (MSE)
analysis of LDF signals in healthy subjects, showed a similar behaviour of the MSE
of the BF signal when filtered for the frequencies associated with heart rate (∼0.6–
2 Hz). These authors suggested that the increase and then decrease of the MSE over
the scales may be due to the non-periodic nature of the signals and therefore the
progression of complexity in multiple scales cannot be stable [41].
19.6 Other Descriptors of Time- and Frequency-Domain
Characteristics of the Microvascular Blood Flux
Signal
There are a growing number of publications on the analysis of other time and
frequency characteristics of LDF signals. For example, empirical mode decomposition is a method of decomposing a signal in the time domain, which may be nonlinear
and non-stationary, into a set of functions allowing the varying frequencies in time
to be preserved. Humeau-Heurtier and Klonizakis [42] used this approach to find
instantaneous frequencies from intrinsic mode functions, in healthy subjects and
patients with varicose veins. Liao and Jan [51] analysed nonlinear properties of
LDF signals in subjects at risk of pressure ulcers using ensemble empirical mode
decomposition to examine the self-phase synchronisation between the component
frequencies of blood flow oscillations. However, two of the most promising areas
of current investigation are time localised phase coherence and the use of attractor
reconstruction.
19.6.1 Time Localised Phase Coherence
Phase coherence is another approach to studying interactions between different
time series. High phase coherence synchronisation can be understood as connectivity/congruence between studied signals. This approach has been applied by
Bernjak et al. [9] to simultaneously recorded skin blood flux and tissue oxygenation signals measured at the forearm of healthy volunteers. The phase coherence was
estimated as the difference in instantaneous phases at each frequency and each time
point, using a wavelet transform. A major finding using this approach was that the
phase difference changed over time and with the microvascular bed sampled. The
authors observed a significant phase coherence between the two signals in the low
frequencies and also in the cardiac frequency band in the superficial dermal vascular
bed. They reported no significant phase coherence in deeper tissues [9]. Similarly,
Tankanag et al. [82] investigating wavelet phase coherence of oscillations between
M. Thanaj et al.
However, entropy measures do not show the same changes through scales as
complexity. Humeau et al. [41] in a recent study of the multiscale entropy (MSE)
analysis of LDF signals in healthy subjects, showed a similar behaviour of the MSE
of the BF signal when filtered for the frequencies associated with heart rate (∼0.6–
2 Hz). These authors suggested that the increase and then decrease of the MSE over
the scales may be due to the non-periodic nature of the signals and therefore the
progression of complexity in multiple scales cannot be stable [41].
19.6 Other Descriptors of Time- and Frequency-Domain
Characteristics of the Microvascular Blood Flux
Signal
There are a growing number of publications on the analysis of other time and
frequency characteristics of LDF signals. For example, empirical mode decomposition is a method of decomposing a signal in the time domain, which may be nonlinear
and non-stationary, into a set of functions allowing the varying frequencies in time
to be preserved. Humeau-Heurtier and Klonizakis [42] used this approach to find
instantaneous frequencies from intrinsic mode functions, in healthy subjects and
patients with varicose veins. Liao and Jan [51] analysed nonlinear properties of
LDF signals in subjects at risk of pressure ulcers using ensemble empirical mode
decomposition to examine the self-phase synchronisation between the component
frequencies of blood flow oscillations. However, two of the most promising areas
of current investigation are time localised phase coherence and the use of attractor
reconstruction.
19.6.1 Time Localised Phase Coherence
Phase coherence is another approach to studying interactions between different
time series. High phase coherence synchronisation can be understood as connectivity/congruence between studied signals. This approach has been applied by
Bernjak et al. [9] to simultaneously recorded skin blood flux and tissue oxygenation signals measured at the forearm of healthy volunteers. The phase coherence was
estimated as the difference in instantaneous phases at each frequency and each time
point, using a wavelet transform. A major finding using this approach was that the
phase difference changed over time and with the microvascular bed sampled. The
authors observed a significant phase coherence between the two signals in the low
frequencies and also in the cardiac frequency band in the superficial dermal vascular
bed. They reported no significant phase coherence in deeper tissues [9]. Similarly,
Tankanag et al. [82] investigating wavelet phase coherence of oscillations between