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      Mathematical biomarkers for the autonomic regulation of cardiovascular system

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          Abstract

          Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance.

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          Most cited references73

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          Approximate entropy as a measure of system complexity.

          Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.
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            Heart rate variability: a review.

            Heart rate variability (HRV) is a reliable reflection of the many physiological factors modulating the normal rhythm of the heart. In fact, they provide a powerful means of observing the interplay between the sympathetic and parasympathetic nervous systems. It shows that the structure generating the signal is not only simply linear, but also involves nonlinear contributions. Heart rate (HR) is a nonstationary signal; its variation may contain indicators of current disease, or warnings about impending cardiac diseases. The indicators may be present at all times or may occur at random-during certain intervals of the day. It is strenuous and time consuming to study and pinpoint abnormalities in voluminous data collected over several hours. Hence, HR variation analysis (instantaneous HR against time axis) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system. Computer based analytical tools for in-depth study of data over daylong intervals can be very useful in diagnostics. Therefore, the HRV signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. In this paper, we have discussed the various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV.
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              Prospective Study of Heart Rate Variability and Mortality in Chronic Heart Failure: Results of the United Kingdom Heart Failure Evaluation and Assessment of Risk Trial (UK-Heart)

              Patients with chronic heart failure (CHF) have a continuing high mortality. Autonomic dysfunction may play an important role in the pathophysiology of cardiac death in CHF. UK-HEART examined the value of heart rate variability (HRV) measures as independent predictors of death in CHF. In a prospective study powered for mortality, we recruited 433 outpatients 62+/-9.6 years old with CHF (NYHA functional class I to III; mean ejection fraction, 0.41+/-0.17). Time-domain HRV indices and conventional prognostic indicators were related to death by multivariate analysis. During 482+/-161 days of follow-up, cardiothoracic ratio, SDNN, left ventricular end-systolic diameter, and serum sodium were significant predictors of all-cause mortality. The risk ratio for a 41.2-ms decrease in SDNN was 1.62 (95% CI, 1.16 to 2.44). The annual mortality rate for the study population in SDNN subgroups was 5.5% for >100 ms, 12.7% for 50 to 100 ms, and 51.4% for <50 ms. SDNN, creatinine, and serum sodium were related to progressive heart failure death. Cardiothoracic ratio, left ventricular end-diastolic diameter, the presence of nonsustained ventricular tachycardia, and serum potassium were related to sudden cardiac death. A reduction in SDNN was the most powerful predictor of the risk of death due to progressive heart failure. CHF is associated with autonomic dysfunction, which can be quantified by measuring HRV. A reduction in SDNN identifies patients at high risk of death and is a better predictor of death due to progressive heart failure than other conventional clinical measurements. High-risk subgroups identified by this measurement are candidates for additional therapy after prescription of an ACE inhibitor.
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                Author and article information

                Journal
                Front Physiol
                Front Physiol
                Front. Physiol.
                Frontiers in Physiology
                Frontiers Media S.A.
                1664-042X
                12 August 2013
                07 October 2013
                2013
                : 4
                : 279
                Affiliations
                [1] 1Center of Innovation, Technology and Education–(CITE), Camilo Castelo Branco University (UNICASTELO) Sao Jose dos Campos, Brazil
                [2] 2Department of Automation and Systems Technology, Federal Institute of Science and Technology of Sao Paulo Sao Jose dos Campos, Brazil
                [3] 3Department of Physiology, Sultan Qaboos University Muscat, Oman
                [4] 4Institute of Electronics and Telematics Engineering of Aveiro, University of Aveiro Aveiro, Portugal
                Author notes

                Edited by: Geoffrey A. Head, Baker IDI Heart and Diabetes Institute, Australia

                Reviewed by: Alessandro Silvani, Università di Bologna, Italy; Elena Lukoshkova, Russian Cardiology Research and Production Complex, Russia

                *Correspondence: Luciana A. Campos, Center of Innovation, Technology and Education–(CITE), Camilo Castelo Branco University (UNICASTELO), Sao Jose dos Campos Technology Park, Presidente Dutra Road Km 138, Sao Jose dos Campos, SP 12247-004, Brazil e-mail: camposbaltatu@ 123456yahoo.com

                This article was submitted to Integrative Physiology, a section of the journal Frontiers in Physiology.

                Article
                10.3389/fphys.2013.00279
                3791874
                24109456
                0e67dfaa-8739-4d84-8536-e8ce2d02f726
                Copyright © 2013 Campos, Pereira, Muralikrishna, Albarwani, Brás and Gouveia.

                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) or licensor 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.

                History
                : 30 July 2013
                : 17 September 2013
                Page count
                Figures: 3, Tables: 1, Equations: 3, References: 88, Pages: 9, Words: 7698
                Categories
                Physiology
                Review Article

                Anatomy & Physiology
                heart rate variability,cardiovascular system,mathematical modeling,fuzzy logic,nonlinear dynamics,linear models,baroreflex

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