Complexity Analysis and Complexity Loss in Physiological Systems: Advances and Applications

Topic summary: This collection of articles explores sophisticated non-linear methods and fractal analyses applied to physiological and clinical signals across different contexts and species. Central themes include the multidimensional and fractal-like nature of physiological signals, the adaptive control of posture through sensory feedback modulated by fractal characteristics, and the role of non-linear dynamic analyses in clinical diagnostics and risk prediction. Research demonstrates how dexterous postural control exhibits adaptable fractal scaling effects influenced by sensory factors and head orientations, highlighting fractality as an adaptive physiological control mechanism. Another study theoretically associates multi-scale physiological networks displaying characteristic 1/f scaling with thermodynamic and energy-balance constraints through ensembles of dissipative oscillators. Clinical studies further emphasize the applicability of nonlinear methodologies, illustrating that measures such as sample entropy of intraoperative cerebral oxygenation can predict postoperative cognitive outcomes. Similarly, nonlinear heart rate variability indices provide valuable biomarkers for assessing the severity of obstructive sleep apnea and associated cardiovascular risk, demonstrating reduced physiological complexity in disease states. Together, these studies underscore the versatility and significance of fractal and non-linear analyses in enhancing our understanding of complex physiological dynamics and their implications for health assessment and treatment.
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Complexity is a concept that encompasses the way living systems adapt to daily life situations and stress, preserving the so-called homeostasis, by the nonlinear interactions of underlying physiological networks, regulatory mechanisms and feedback loops operating on a range of temporal and spatial scales, often characterized by fractal structures. The dynamics of physiological systems is reflected in fluctuations of the different biological signals they generate. Consequently, the complexity analysis of these signals may allow estimating the adaptability of biological systems in response to changes of internal and external inputs.

Complexity is generally assessed on short-term physiological signals with approaches that emerge from information theory based on the Shannon entropy, as approximate or sample entropy, among others. However, the former metrics may lead to erroneous interpretations as entropy increases as the signal randomness increases. An example is atrial fibrillation, which increases the sample entropy of beat-by-beat heart rate variability, in stark contrast with the paradigm of the loss complexity in disease and aging. To circumvent the problem, it has been proposed to measure the “structural richness” of a signal calculating the entropy at several time scales separately, giving rise to the method of multiscale entropy.

Although complexity indices based on univariate multiscale entropy provided interesting and helpful biomarkers in health and disease, it has been recognized recently the relevance to include multivariate signals to gain a deeper understanding of physiological phenomena and estimate the complexity of physiological networks. Systems adaptability also depends upon physiological inter-dependent dynamic interactions among subsystems, leading to highly complex variations. In this sense, the meaning of complexity has been extended, and new developments have emerged as the multiscale transfer entropy, the analysis of information flow between temporal-scales, and multiscale fractality. Furthermore, complexity has been evaluated from interacting physiological processes that may have different temporal dynamics. Considering all the potential exciting advances in the analysis of systems complexity and adaptability, the goal of this research topic is to focus on emerging approaches for estimating complexity using multivariate signals, transfer entropy and information flow, particularly based on multiscale assessments, and hopefully, to clarify causes of complexity loss in physiological networks. Also, applications are welcome in diverse physiological systems under different pathological conditions, as well as tutorials and reviews in the field.

We welcome original articles, opinion and review papers, and multidisciplinary contributions in the field of complexity and complexity loss analysis in network physiology, with topics focused on, but not limited to:

• Emerging theoretical approaches to analyze complexity and complexity loss in a multiscale information theory framework.
• Complexity estimation based on multiscale analysis of multivariate time series.
• Complexity estimation based on multivariate schemes for interscale analysis.
• Application of complexity methods and analysis of complexity loss in diseases and diverse clinical states such as sleep disorders, neurological diseases (e.g., depression), orthostatic intolerance, heart failure, cognitive dysfunctions, pulmonary diseases, and respiratory failure, among others.

Keywords: Complexity, time scales, spatial scales, information transfer, cardiovascular variability, respiratory variability, EEG, EMG, physiological oscillations, brain networks, network physiology, non-linear dynamics, fractal analysis

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