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Edited and reviewed by: Zbigniew R. Struzik, The University of Tokyo, Japan

This article was submitted to Fractal and Network Physiology, a section of the journal Frontiers in Physiology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

A fundamental problem in biology, physiology, and medicine is understanding how complexity in the structure and dynamics of biological and physiological systems emerges from multicomponent regulatory mechanisms, where non-linear feedback loops across scales lead to efficient homeostatic control in the presence of continuous temporal variability in systems outputs. Addressing this problem requires (i) comprehensive analyses of systems dynamics based on multifractal formalism and methodology (Ivanov et al.,

Despite the increased need for smart healthcare sensing systems that monitor patients' body balance, there is no coherent theory that facilitates the modeling of human physiological processes and the design and optimization of future healthcare cyber-physical systems (HCPSs) (Bogdan and Marculescu,

To maintain good health, prevent health complications, and/or avoid fatal conditions calls for a cross-disciplinary approach to HCPS design that rely on recent advances in statistical physics, non-linear dynamics, machine learning, and artificial intelligence. There is a palpable need for a multi-disciplinary approach to consolidate the current state of art in order to respond to the following fundamental challenges. First and foremost, the fundamental properties (e.g., non-stationarity, fractality) of human physiology in terms of mathematical formalism needs to be characterized in order to facilitate the understanding of its complexity (West,

Indeed, defining the trajectory of the healthy aging process in terms of its complexity metrics (Goldberger et al.,

With the goal of mathematical characterization of blood glucose variability, initially scrutinized in Ghorbani and Bogdan (

In order to extract the multifractal characteristics and determine disease signatures,

To provide a deeper understanding of atrial fibrillation disease,

We need rigorous mathematical techniques and a general theoretical framework to characterize the interactions between integrated physiologic systems with different output dynamics (Bartsch et al.,

Finally, there is a fundamental need for deeper understanding of the mechanisms of stochastic feedback and variability in biological systems and physiological processes (Ivanov et al.,

The works presented in this Research Topic collection as well as current advances in the field of fractal and multi-fractal investigations of physiological systems structure and dynamics, and their applications to homeostatic control, clinical diagnosis, and the development of cyber-physical systems in healthcare outline a new horizon of multidisciplinary cooperation with new challenges. There is an urgent need for adopting a cross-scale perspective and a corresponding theoretical framework to investigate the multi-scale regulatory mechanisms underlying the overall network physiology and its relation to physiological states and functions emerging at the organism level in health and disease. When dealing with the heterogeneity, multi-modality and complexity of physiological processes, we need rigorous mathematical and algorithmic techniques that can extract causal interdependencies between systems across different scales while overcoming various noise sources. For example, obtaining high-frequency genomic and proteomic sensing data over large spatial and temporal dimensions can open new frontiers and lead to the discovery of basic laws of regulation with broad clinical applications. Consequently, progress in this direction will require new algorithmic strategies to quantify time-varying information flow among diverse physiological processes across scales, and determine how it influences the global dynamics of complex physiological networks. Intrinsically related with future efforts on quantifying causal dependencies and control principles in biological and physiological networks, it will be essential to develop robust optimization algorithms capable to reconstruct or infer the structure and dynamics of complex interdependent networks while overcoming partial observability, noise induced defects and adversarial interventions caused by bacterial or viral infections. Lastly, the biomedical and engineering communities need to develop new control methodologies that do not seek to only enforce a specific reference value (that proved beneficial for some patients), but rather ensure that the physiological complexity and multifractality are restored to the healthy profiles when abnormalities are detected—e.g., a mathematical strategy to abstract the complexity of brain network through an approximate transfer function and a new minimal control strategy allows one to efficiently enforce a healthy fractal profile when frailty is early detected.

Toward this end, with these challenges also unique opportunities arise for interdisciplinary research. From the interactions of statistical physics, non-linear dynamics, information theory, probability and stochastic processes, artificial intelligence, machine learning, control theory and optimization, basic physiology and medicine new theoretical and algorithmic foundations will emerge for mining, analyzing, and controlling the network physiology. Ultimately, such efforts would lead to a new class of network-physiology-derived diagnostic and prognostic markers with innovative applications in cyber-physical systems and clinical practice.

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We acknowledge support from several funding agencies: PB acknowledges the support by the National Science Foundation (NSF) under the Career Award CPS/CNS-1453860, CCF-1837131, MCB-1936775, CNS-1932620, and CMMI-1936624, the U.S. Army Defense Advanced Research Projects Agency (DARPA) under grant number W911NF-17-1-0076, and the DARPA Young Faculty Award and Director's Fellowship Award under grant number N66001-17-1-4044; AE acknowledges the support by the Department of Physiology, Semmelweis University; PChI thanks the W. M. Keck Foundation, National Institutes of Health Grant 1R01-HL098437, Office of Naval Research Grant 000141010078, US-Israel Binational Science Foundation Grant 2012219 for support. The funders had no role in decision to publish or preparation of the manuscript.