Fractal Analysis of Cardiovascular Signals Empowering the Bioengineering Knowledge

Abstract

The cardiovascular system is composed of a complex network of vessels, where highly uniform hierarchical branching structures are regulated by the anatomy and local flow requirements. Arteries bifurcate many times before they become capillaries where the scaling factor of vessel length, diameter and angle between two children branches is established at each level of recurrence. This behaviour can be easily described using a fractal scaling principle. Moreover, it was observed that the basic pattern of blood distribution is also fractal, imposed both by the anatomy of the vascular tree and the local regulation of vascular tone. In this chapter, arterial physiology was analysed, where waveform complexity of arterial pressure time series was related to arterial stiffness changes, pulse pressure variations and the presence wave reflection. Fractal dimension was used as a nonlinear measure, giving place to a 'holistic approach of fractal dimension variations throughout the arterial network', both in health and disease.

Increased brain microvascular hemoglobin concentrations in children with cerebral malaria

“…This property indicates long-range correlation, meaning signal fluctuations at a given time influence dynamics up to several minutes in the future. For example, a self-similar signal moving in a positive direction will tend to continue that trend (33). Complex systems in physics and biology tend to evolve toward this self-organized fractal state.…”

“…These periodic fluctuations give rise to emergent fractal properties of the signal, such as self-similarity. A signal is self-similar when it can be split into smaller fragments that retain features of the original signal at a different time scale (32)(33)(34). Detrended fluctuation analysis (DFA) characterizes longrange self-similarity in the structure of a signal over time (35,36).…”

“…Signals with high levels of randomness have an α value of around 0.5, whereas those that are increasingly selfsimilar approach 1.0. DFA has been used to characterize cardiovascular signals (32,33), neuronal oscillations (34,(37)(38)(39), intracranial pressure abnormalities (40), and cerebral regulation in other brain injury contexts (28,(41)(42)(43)(44), and here we apply this approach to cerebral malaria.…”

New Hemodynamic Parameters in Peri-Operative and Critical Care—Challenges in Translation

“…In particular, significant evidence on the importance of active arterial regulation mechanisms has been found. Studies are revealing the complex, dynamic behavior of arteries on local as well as systemic levels [ 19 , 54 , 55 ]. Since early observations on the ability of vessels to constrict/distend, evidence about other mechanisms has been found: pulse propagation, systemic resistance, local flow, and wave reflection are controlled via factors such as the non-linear properties of the arterial wall, viscosity, damping properties, frequency-dependent behavior, and strain-dependent activation of the smooth muscle tone [ 19 ].…”

Quantitative Vascular Evaluation: From Laboratory Experiments to Point-of-Care Patient (Experimental Approach)

“…The effect of arterial tree structure on arterial pressure fractal behavior was assessed on laboratory animals in [ 21 , 44 ].…”