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Open AccessArticle

Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series

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Faculdade de Ciências, Universidade do Porto, Rua Campo Alegre, 4169-007 Porto, Portugal
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Centro de Matemática da Universidade do Porto (CMUP), 4169-007 Porto, Portugal
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Department of Engineering, University of Palermo, Viale delle Scienze, Bldg. 9, 90128 Palermo, Italy
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Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, 4169-007 Porto, Portugal
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Centro de Investigação e Desenvolvimento em Matemática e Aplicações (CIDMA)
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Department of Physiology, Comenius University in Bratislava, Jessenius Faculty of Medicine, Mala Hora 4C, 03601 Martin, Slovakia
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Biomedical Center Martin, Comenius University in Bratislava, Jessenius Faculty of Medicine, Mala Hora 4C, 03601 Martin, Slovakia
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(3), 315; https://doi.org/10.3390/e22030315
Received: 18 February 2020 / Revised: 9 March 2020 / Accepted: 9 March 2020 / Published: 11 March 2020
(This article belongs to the Special Issue Multiscale Entropy Approaches and Their Applications)
Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations. View Full-Text
Keywords: multi-scale entropy (MSE); vector autoregressive fractionally integrated (VARFI) models; heart rate variability (HRV); systolic arterial pressure (SAP) multi-scale entropy (MSE); vector autoregressive fractionally integrated (VARFI) models; heart rate variability (HRV); systolic arterial pressure (SAP)
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Martins, A.; Pernice, R.; Amado, C.; Rocha, A.P.; Silva, M.E.; Javorka, M.; Faes, L. Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series. Entropy 2020, 22, 315.

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