19 Complexity-Based Analysis of Microvascular Blood …
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19.3.1 Fast Fourier Transform
The Fourier Transform (FT) is the decomposition of a time series into its constituent
frequency components [29, 62]. Power Spectral Density (PSD) describes the contribution to the power in the frequency components across a spectrum. In FFT analysis,
the PSD of flow motion waves is obtained by computing the discrete Fourier transform of the LDF signal, which itself is a discrete representation of a continuous
signal. In this way FFT analysis provides an estimate of the absolute power in the
signal at a given frequency and of the PSD contribution of a frequency band to the
total power of the signal. This is often used to evaluate the impact of each frequency
band (and their associated control mechanisms) on overall flowmotion.
19.3.2 Wavelet Transform
Generalized wavelet analysis is a scale-independent method with adjustable time
and frequency resolution. It was introduced for the analysis of LDF signals by
Stefanovska and colleagues [8]. While wavelets are not specifically designed for
spectral analysis, spectral information can be recovered by analysis of the wavelets
to produce the scalogram giving the energy contribution of each wavelet coefficient
which can then be used to express the flow motion activities in AU/Hz [79]. The
Wavelet Transform (WT) allows for the analysis of time and frequency contents of
an oscillatory signal [56] and has the advantage over the FFT in that it provides
information about changes in frequency and power of distinct oscillatory bands over
time. The WT can also be averaged over time, at a particular frequency, to yield an
average scalogram.
19.3.3 Application of Spectral Domain Analysis
Spectral analysis of the low frequency periodic oscillations in blood flux measurements obtained using LDF provides mechanistic information of the processes regulating microvascular perfusion [45, 71, 79]. A decline in microvascular function is
widely associated with variations in the amplitude and relative contribution of the
low frequency oscillations, with flow patterns differing according to the time course
and severity of disease [57, 65, 66]. There is, however, a lack of consensus on the
interpretation of the direction of change of the relative contributions of the oscillatory signals across the spectral bands and their mechanistic origins. Direct comparison of different studies is complicated by the choice of parameters for frequency
domain analysis (e.g. window size, overlap, number of bins). Furthermore, recent
work suggests that the frequency bands are not fixed and may vary, for example,
with age or pathological state [33]. Most studies use fixed non-overlapping intervals
295
19.3.1 Fast Fourier Transform
The Fourier Transform (FT) is the decomposition of a time series into its constituent
frequency components [29, 62]. Power Spectral Density (PSD) describes the contribution to the power in the frequency components across a spectrum. In FFT analysis,
the PSD of flow motion waves is obtained by computing the discrete Fourier transform of the LDF signal, which itself is a discrete representation of a continuous
signal. In this way FFT analysis provides an estimate of the absolute power in the
signal at a given frequency and of the PSD contribution of a frequency band to the
total power of the signal. This is often used to evaluate the impact of each frequency
band (and their associated control mechanisms) on overall flowmotion.
19.3.2 Wavelet Transform
Generalized wavelet analysis is a scale-independent method with adjustable time
and frequency resolution. It was introduced for the analysis of LDF signals by
Stefanovska and colleagues [8]. While wavelets are not specifically designed for
spectral analysis, spectral information can be recovered by analysis of the wavelets
to produce the scalogram giving the energy contribution of each wavelet coefficient
which can then be used to express the flow motion activities in AU/Hz [79]. The
Wavelet Transform (WT) allows for the analysis of time and frequency contents of
an oscillatory signal [56] and has the advantage over the FFT in that it provides
information about changes in frequency and power of distinct oscillatory bands over
time. The WT can also be averaged over time, at a particular frequency, to yield an
average scalogram.
19.3.3 Application of Spectral Domain Analysis
Spectral analysis of the low frequency periodic oscillations in blood flux measurements obtained using LDF provides mechanistic information of the processes regulating microvascular perfusion [45, 71, 79]. A decline in microvascular function is
widely associated with variations in the amplitude and relative contribution of the
low frequency oscillations, with flow patterns differing according to the time course
and severity of disease [57, 65, 66]. There is, however, a lack of consensus on the
interpretation of the direction of change of the relative contributions of the oscillatory signals across the spectral bands and their mechanistic origins. Direct comparison of different studies is complicated by the choice of parameters for frequency
domain analysis (e.g. window size, overlap, number of bins). Furthermore, recent
work suggests that the frequency bands are not fixed and may vary, for example,
with age or pathological state [33]. Most studies use fixed non-overlapping intervals