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      Effect of Age on Complexity and Causality of the Cardiovascular Control: Comparison between Model-Based and Model-Free Approaches

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          The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related modifications of complexity and causality in healthy humans in supine resting (REST) and during standing (STAND). We found that: 1) MF approaches are more efficient than the MB method when nonlinear components are present, while the reverse situation holds in presence of high dimensional embedding spaces; 2) the CE method is the least powerful in detecting age-related trends; 3) the association of HP complexity on age suggests an impairment of cardiac regulation and response to STAND; 4) the relation of SAP complexity on age indicates a gradual increase of sympathetic activity and a reduced responsiveness of vasomotor control to STAND; 5) the association from SAP to HP on age during STAND reveals a progressive inefficiency of baroreflex; 6) the reduced connection from HP to SAP with age might be linked to the progressive exploitation of Frank-Starling mechanism at REST and to the progressive increase of peripheral resistances during STAND; 7) at REST the diminished association from RESP to HP with age suggests a vagal withdrawal and a gradual uncoupling between respiratory activity and heart; 8) the weakened connection from RESP to SAP with age might be related to the progressive increase of left ventricular thickness and vascular stiffness and to the gradual decrease of respiratory sinus arrhythmia.

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          Most cited references 62

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              Approximate entropy (ApEn) as a complexity measure.

               S Pincus (1995)
              Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity, which appears to have potential application to a wide variety of relatively short (greater than 100 points) and noisy time-series data. The development of ApEn was motivated by data length constraints commonly encountered, e.g., in heart rate, EEG, and endocrine hormone secretion data sets. We describe ApEn implementation and interpretation, indicating its utility to distinguish correlated stochastic processes, and composite deterministic/ stochastic models. We discuss the key technical idea that motivates ApEn, that one need not fully reconstruct an attractor to discriminate in a statistically valid manner-marginal probability distributions often suffice for this purpose. Finally, we discuss why algorithms to compute, e.g., correlation dimension and the Kolmogorov-Sinai (KS) entropy, often work well for true dynamical systems, yet sometimes operationally confound for general models, with the aid of visual representations of reconstructed dynamics for two contrasting processes. (c) 1995 American Institute of Physics.

                Author and article information

                Role: Editor
                PLoS One
                PLoS ONE
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                24 February 2014
                : 9
                : 2
                [1 ]Department of Biomedical Sciences for Health, University of Milan, Milan, Italy
                [2 ]Galeazzi Orthopedic Institute, Milan, Italy
                [3 ]Department of Physics and BIOtech, University of Trento, Trento, Italy
                [4 ]Gruppo Ospedaliero San Donato Foundation, Milan, Italy
                [5 ]Department of Electronics Information and Bioengineering, Politecnico di Milano, Milan, Italy
                [6 ]Department of Anesthesia and Intensive Care, Humanitas Clinical and Research Center, Rozzano, Italy
                [7 ]Humanitas Clinical and Research Center, Rozzano, Italy
                [8 ]BIOtech, Department of Industrial Engineering, University of Trento, Trento, Italy
                [9 ]IRCS PAT-FBK, Trento, Italy
                [10 ]Department of Physiotherapy, Federal University of São Carlos, São Carlos, São Paulo State, Brazil
                University of Adelaide, Australia
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: AP ACMT AMC. Performed the experiments: NMP JM VM ABS ACMT AMC. Analyzed the data: AP VB AM TB NMP JM VM ABS ACMT AMC. Contributed reagents/materials/analysis tools: AP VB AM TB. Wrote the paper: AP LF GN ACMT AMC.


                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                Page count
                Pages: 14
                This study was supported by the São Paulo Foundation for Research Support/Brazil (FAPESP, process number 2010/52070-4), and CAPES (AUXPE-CSF-PVES-2619/2013 process number 23028.007721/2013-41). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Research Article
                Biomedical engineering
                Signal processing
                Statistical signal processing
                Applied mathematics
                Anatomy and physiology
                Cardiovascular system
                Circulatory physiology
                Physiological processes
                Integrative physiology
                Vascular biology



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