Complexity of flow motion

Abstract

The analysis of complex physiologic time series has been the focus of considerable attention since simple mathematical models cannot be found to describe them. Signals derived from skin microvascular networks using Laser Doppler flowmetry (LDF) have been broadly investigated using both linear and nonlinear dynamical methods providing significant information about the microvascular function. This study aims to explore complexity methods that can quantify the changes in the complex flow motion characteristics from the human microcirculation in a range of pathophysiological states. Time and frequency domain analysis were used to define the signal values from the microvascular perfusion and their power contribution using the spectral analysis to quantify the different properties modulating the network perfusion. Nonlinear complexity methods were used to quantify the signal regularity by evaluating the presence of repeated patterns providing complexity variants at single and across multiple spatial and temporal scales. Further, a new approach, attractor reconstruction analysis, was used providing quantitative measures of the microvascular system in phase space and a visual representation in the shape and variability of the signal producing a two-dimensional attractor with features like density and symmetry. The skin blood flux (BF) and tissue oxygenation (OXY) signals obtained from a combined Laser Doppler flowmetry (LDF) and white light spectroscopy (WLS) device were investigated using time domain, frequency domain and the nonlinear methods in the skin of a healthy cohort during increased local warming. This study revealed multiple oscillatory components with a remarkable increase in the cardiac activity during thermally induced vasodilation. There was also shown a significant attenuation in the complexity across multiple scales and a significant drop in the attractor density measures during increased local warming. Subsequently, both linear and nonlinear methods were used to investigate the LDF signals obtained from groups of individuals at an increased cardiovascular disease (CVD) risk, categorised with presence or absence of type 2 diabetes and use of calcium channel blocker (CB) medication. The results showed an increase on the high frequency cardiac activity with CB treatment. There was a significant decrease in the complexity of the blood flux signals as the CVD risk increases across multiple time scales. Also, there is a decline with progression of CVD risk in the measures derived from attractor reconstruction analysis. The highest separability between these groups was achieved using the attractor and complexity measures combined. In conclusion, time and frequency domain analysis alone were insufficient to estimate the complex dynamics of the microvascular network during the application of a standard stressor. Nonlinear analysis provides a better characterisation of the flexibility of the system in a range of pathophysiological conditions. Together these mathematical approaches were able to quantify different microvascular functional states. With machine learning techniques this should allow the classification of the tissue perfusion features providing a use for clinical assessment