Nonlinearity in Living Systems: Theoretical and Practical Perspectives on Metrics of Physiological Signal Complexity

The biological basis of physiological signals is incredibly complex. While many researches certainly appreciate molecular, cellular and systems approaches to unravel overall biological complexity, in the recent decades the interest for mathematical and computational characterization of structural and functional basis underlying biological phenomena gain wide popularity among scientists. Indeed, the earliest descriptions of physiological signals were purely phenomenological, with elegant description of functional changes in space and time. Nowadays, we witnessed wide range applications of nonlinear quantitative analysis that produced measures such as fractal dimension, power law scaling, Hurst exponent, Lyapunov exponent, approximate entropy, sample entropy, Lempel–Ziv complexity as well as other metrics for predictions of onset and progression of many pathological conditions, especially in the central nervous systems (CNS). In addition to dramatic improvement in understanding of normal and abnormal human physiology, also there is another fundamental task of getting straight what physiological signals might reveal about the evolution and functional integration of biological hierarchies throughout animal kingdom in the first place. Besides finding its place for spiking activity, neurotransmitter release, ion channel activity, local field potential (LFP), electroencephalography (EEG), electrocorticography (ECoG), electromyography (EMG), electrocardiography (ECG) and fMRI signals analysis in humans and other mammals, one of the goals of biological nonlinear dynamics is to provide comparative and evolutionary perspectives on various physiological functions. Indeed, there are attempts to extend their application not only to varying experimental and medical conditions but also to quantify neural interactions in phylogenetically distant species of organisms. Also there is another more theoretical challenge of contemporary nonlinear signal measurements, especially including fractal-based methods. The question of choosing the right method and its possible adjustment in order for the results of the analysis to be as accurate as possible is the persistent problem.

In this Research Topic, we seek to bring together the recent practical and theoretical advances in the development and application of nonlinear methods or narrower fractal-based methods for characterizing the complex physiological systems at multiple levels of organization. We will discuss the use of various complexity measures and appropriate parameters for characterizing the variety of physiological signals from molecular to systems level. There are multiple aims of this topic. The recent advancement in application of nonlinear methods for both normal and pathological physiological conditions will be the first. The second aim is to emphasize the more recent successful attempt to apply these methods across animal species. Finally, a comprehensive understanding of advantages and disadvantages of each method, especially between its mathematical assumptions and real-world applicability, can help to find out what is at stake regarding the above aims and to direct us toward more fruitful application of nonlinear measures and statistics in physiology and biology in general.

Our intention, in this Research Topic, is to enable an international and multidisciplinary forum for researchers to bring out the recent developments in their research areas through original research papers in the three categories: (1) novel fractal-based or nonlinear methods and/or their applications in the analysis of physiological signals in the original research paper form, (2) surveys of recent progress in a specific sub-area and (3) comprehensive review articles with a tutorial function.