Multiscale, multidomain analysis of microvascular flow dynamics

What is the topic of this review? We describe a range of techniques in the time, frequency and information domains and their application alone and together for the analysis of blood flux signals acquired using laser Doppler fluximetry. What advances does it highlight? This review highlights the idea of using quantitative measures in different domains and scales to gain a better mechanistic understanding of the complex behaviours in the microcirculation.


INTRODUCTION
Investigations of blood flow in microvascular networks have shown that in many disease states, such as cardiovascular and metabolic disease, there is a reduction in the adaptive capabilities of the network and its ability to respond to an imposed stressor (Frisbee et al., 2016). The processes underlying the modulation of the blood flow are known to operate at different intensity levels and have different periodicities (Stefanovska, Bracic, & Kvernmo, 1999), which can change both temporally and spatially. Conventional time-and frequency-domain analysis techniques have proved valuable in the understanding of the network blood flow but have, so far, failed to describe mechanistically the changes in observed flow patterns between pathological conditions or haemodynamic states. Recently, non-linear methods based on ideas from information theory have been used to quantify the regularity and randomness of short lengths of physiological signals and have demonstrated the potential for diagnostic capability (Balasubramanian & Nagaraj, 2016). These This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. The aim of this brief report is to describe the application of a range of analysis techniques to signals derived from skin blood flow.
We review the main applications and considerations of approaches in the time, frequency and complexity domains and their use in combination to discriminate between microcirculatory blood flow signals in differing pathophysiological and/or haemodynamic states.
Examples are taken from two groups of individuals at risk of cardiovascular and metabolic disease that we have reported previously in detail elsewhere (Chipperfield, Thanaj, Scorletti, Byrne, & Clough, 2019), grouped for the use (CB1, n = 8) or not (CB0, n = 28) of a calcium channel (CB) blocker for the treatment of hypertension.
Calcium channel blockers are considered here because they are vasodilators that, in particular, inhibit myogenic control and can thus be expected to result in altered microvascular flow dynamics, against which the different analysis methods may be tested. and cardiac activity (0.4-1.6 Hz) activity (Stefanovska et al., 1999) and are usually made from resting BF signals. Two main methods are used

New Findings
• What is the topic of this review?
We describe a range of techniques in the time, frequency and information domains and their application alone and together for the analysis of blood flux signals acquired using laser Doppler fluximetry.

• What advances does it highlight?
This review highlights the idea of using quantitative measures in different domains and scales to gain a better mechanistic understanding of the complex behaviours in the microcirculation.
to assess the spectral contribution of these component signals; one is based on the fast Fourier transform (FFT), the other on generalized wavelet analysis. The choice of method used has been discussed in detail elsewhere (Clough, Kuliga, & Chipperfield, 2017) and is thus not considered further here. With the FFT, the power spectral density of the BF signal is obtained from its discrete Fourier transform (in perfusion units squared per hertz), estimating the absolute power in the signal at a given frequency. Figure 2 shows the power spectrum, calculated using Welch's method, for the two subjects shown in

INFORMATION AND COMPLEXITY
If the signals in Figure 1 could be described accurately by some mathematical model:

FREQUENCY, COMPLEXITY AND SCALE
The physiological processes that regulate flow-motion operate across multiple temporal scales, ranging from 0.001 to 2 Hz, and appear to vary with other parameters, such as skin temperature (Kuliga et al., 2018) and hypobaric hypoxia (Carey et al., 2019). For the data presented above, the LZC index is correlated positively with dilator capacity (MF/RF; r = 0.47, P = 0.001) and relative power in the respiratory band (r = 0.52, P = 0.0001) and negatively with RF (r = −0.37, P = 0.008) and relative power in the cardiac band (r = −0.56, P = 0.00004) (Chipperfield et al., 2019). The regular contribution to the information in the BF signal from the cardiac band, illustrated in Figure 2, appears to reduce the complexity in the CB1 group.
To account for these multiple, and potentially varying, process scales, LZC can be evaluated at multiple time scales (MLZC) using a coarse-graining approach (Cerutti, Hoyer, & Voss, 2009;Costa, Goldberger, & Peng, 2002). The sampling frequency is altered by a scale factor, , defining the scale level used to resample the original signal, reducing the scale of the time series. For the time series where N is the number of samples, the coarse-grained time series, y , is as follows: reported that a signal length > 1000 samples is required (Thanaj et al., 2018), which equates to 10 min captured at 40 Hz at scale = 24.
Such multiscale analyses have been shown to be effective for understanding physiological signals in general (Costa et al., 2002;Humeau et al., 2010). Figure 3b shows an example of MLZC for the two groups, CB0 and CB1. As scale length increases (lower frequency corresponding to higher scale), LZC can also be seen to increase together with the separation between the groups until the Nyquist frequency of the original BF signal is reached or passed. Assuming that the maximal frequency of interest is the upper limit of the cardiac band of 1.6 Hz, the Nyquist frequency will be 3.2 Hz. ( = 12). Above this scale, i.e. with lower sample frequencies, the influence of the relatively periodic heart rate will be diminished, and the signal will contain more information. To reach higher scales would require longer BF recordings. Hz; red) activity and multiscale Lempel-Ziv complexity of skin blood flow signals in n = 28 people without CB (a) and n = 8 people with CB (b). Effective sampling rate = 40 Hz/scale. * P < 0.05, + P < 0.01 is that it can be used to understand how the spectral components of the BF signal influence its complexity at different scales. For example, the Spearman's correlations between the power in each of the bands of the power spectra of the BF signals and the MLZC at increasing scale for the CB1 and CB0 groups described previously are shown in Figure 4. Heart beat and respiration have significant but opposite correlations with complexity until the Nyquist frequency is passed, when their influence reduces. Skin sympathetic nerve activity is known to be modulated by respiration, and cutaneous vasoconstrictor neurones are coupled temporally to cardiac and respiratory oscillations (Fatouleh & Macefield, 2013). Heart rate variability also contributes to the complexity of the BF signal (Sassi et al., 2015), and cardiac rhythm is modulated by respiration (Simms, Paton, Allen, & Pickering, 2010). This coupling of the two high-frequency components might