An easy-to-use technique to characterize cardiodynamics from first-return maps on ΔRR-intervals.

Heart rate variability analysis using 24-h Holter monitoring is frequently performed to assess the cardiovascular status of a patient. The present retrospective study is based on the beat-to-beat interval variations or ΔRR, which offer a better view of the underlying structures governing the cardiodynamics than the common RR-intervals. By investigating data for three groups of adults (with normal sinus rhythm, congestive heart failure, and atrial fibrillation, respectively), we showed that the first-return maps built on ΔRR can be classified according to three structures: (i) a moderate central disk, (ii) a reduced central disk with well-defined segments, and (iii) a large triangular shape. These three very different structures can be distinguished by computing a Shannon entropy based on a symbolic dynamics and an asymmetry coefficient, here introduced to quantify the balance between accelerations and decelerations in the cardiac rhythm. The probability P111111 of successive heart beats without large beat-to-beat fluctuations allows to assess the regularity of the cardiodynamics. A characteristic time scale, corresponding to the partition inducing the largest Shannon entropy, was also introduced to quantify the ability of the heart to modulate its rhythm: it was significantly different for the three structures of first-return maps. A blind validation was performed to validate the technique.

Automatic sleep staging from ventilator signals in non-invasive ventilation.

Non-invasive ventilation (NIV), a recognized treatment for chronic hypercapnic respiratory failure, is predominantly applied at night. Nevertheless, the quality of sleep is rarely evaluated due to the required technological complexity. A new technique for automatic sleep staging is here proposed for patients treated by NIV. This new technique only requires signals (airflow and hemoglobin oxygen saturation) available in domiciliary ventilators plus a photo-plethysmogram, a signal already managed by some ventilators. Consequently, electroencephalogram, electrooculogram, electromyogram, and electrocardiogram recordings are not needed. Cardiorespiratory features are extracted from the three selected signals and used as input to a Support Vector Machine (SVM) multi-class classifier. Two different types of sleep scoring were investigated: the first type was used to distinguish three stages (wake, REM sleep and nonREM sleep), and the second type was used to evaluate five stages (wake, REM sleep, N1, N2 and N3 stages). Patient-dependent and patient-independent classifiers were tested comparing the resulting hypnograms with those obtained from visual/manual scoring by a sleep specialist. An average accuracy of 91% (84%) was obtained with three-stage (five-stage) patient-dependent classifiers. With patient-independent classifiers, an average accuracy of 78% (62%) was obtained when three (five) sleep stages were scored. Also if the PPG-based and flow features are left out, a reduction of 4.5% (resp. 5%) in accuracy is observed for the three-stage (resp. five-stage) cases. Our results suggest that long-term sleep evaluation and nocturnal monitoring at home is feasible in patients treated by NIV. Our technique could even be integrated into ventilators.

Working conditions for safe detection of nonlinearity and noise titration.

Even if noise titration cannot be satisfactorily used to prove the presence of chaos, it can still be used to detect nonlinear component in dynamics. Nevertheless, since the technique have the use of nonlinear models for one-step-ahead predictions, it requires an acute choice of modeling parameters, i.e., the number of terms and the nonlinearity degree of the models. Based on illustrative examples, we propose conditions under which the method of noise titration can be reliably applied to characterize nonlinearity in the time series. It is thus possible to compare different time series and state which one is governed by the strongest nonlinearity. For instance, it is shown that, when there is a single nonlinear term in the equations describing the system, the variable on which it acts can be identified among the others.

Identifying chaos from heart rate: the right task?

Providing a conclusive answer to the question "is this dynamics chaotic?" remains very challenging when experimental data are investigated. We showed that such a task is actually a difficult problem in the case of heart rates. Nevertheless, an appropriate dynamical analysis can discriminate healthy subjects from patients.

Failure in distinguishing colored noise from chaos using the "noise titration" technique.

Identifying chaos in experimental data-noisy data-remains a challenging problem for which conclusive arguments are still very difficult to provide. In order to avoid problems usually encountered with techniques based on geometrical invariants (dimensions, Lyapunov exponent, etc.), Poon and Barahona introduced a numerical titration procedure which compares one-step-ahead predictions of linear and nonlinear models [Proc. Natl. Acad. Sci. U.S.A. 98, 7107 (2001)]. We investigate the aformentioned technique in the context of colored noise or other types of nonchaotic behaviors. The main conclusion is that in several examples noise titration fails to distinguish such nonchaotic signals from low-dimensional deterministic chaos.

Influence of effluents from a Wastewater Treatment Plant on nutrient distribution in a coastal creek from southern Brazil

The hypothesis that effluents treated through activated sludge process cause changes in nutrient biogeochemistry of receiving water bodies was investigated in Vieira creek, southern Brazil. Dissolved oxygen, suspended matter, and pH did not vary among the sampling stations. Nutrient, biochemical oxygen demand, and conductivity values were significantly higher downstream from the Wastewater Treatment Plant (WWTP) effluents. Further downstream, nitrate concentrations were higher due to ammonium nitrification, organic matter remineralization and/or the occurrence of unidentified sources. Per capita nutrient emission factors were estimated to be 0.16 kg P.yr-1 and 4.14 kg N.yr-1. Under pristine conditions, low N:P ratios were observed, which were significantly increased downstream due to the high ammonium input. The mixing zone of the nitrogen-rich waters from Vieira creek with the phosphorus-enriched waters from Patos lagoon estuary was considered under high risk of eutrophication. The results could be useful for planning and management of WWTP-effluent receiving waters in temperate regions from developing countries.

A hipótese de que efluentes urbanos tratados através de um sistema de lodo ativado causam alterações na qualidade de água de ambientes aquáticos foi investigada no Arroio Vieira, Rio Grande, RS. Amostras de água foram coletadas a montante e a jusante dos emissários de uma estação de tratamento de esgoto (ETE). Oxigênio, material em suspensão e pH não variaram espacialmente. Já os valores para os nutrientes e para a demanda bioquímica do oxigênio foram significativamente maiores a jusante dos efluentes. Mais a jusante, as concentrações de nitrato aumentam devido à nitrificação do nitrogênio amoniacal, remineralização da matéria orgânica e/ou ocorrência de outros aportes não-identificados. A emissão de nutrientes per capita após o tratamento dos efluentes domésticos (0.16 kg P ano-1 e 4.14 kg N ano-1) é elevada. O aporte dos efluentes da ETE causa uma alteração acentuada das razões N:P, sendo os valores maiores a jusante da ETE devido ao aporte preferencial de nitrogênio amoniacal. Os resultados indicam que no local onde as águas do Arroio Vieira, enriquecidas em nitrogênio se misturam com as águas do estuário da Lagoa dos Patos, enriquecidas em fósforo, há grande risco de eutrofização. Os resultados são úteis para o planejamento e gerenciamento de águas receptoras de efluentes em regiões temperadas de paises em desenvolvimento.

Using geometric control and chaotic synchronization to estimate an unknown model parameter.

We present a new parameter estimation procedure for nonlinear systems. Such technique is based on the synchronization between the model and the system whose unknown parameter is wanted. Synchronization is accomplished by controlling the model to make it follow the system. We use geometric nonlinear control techniques to design the control system. These techniques allow us to derive sufficient conditions for synchronization and hence for proper parameter estimation. As an example, this procedure is used to estimate a parameter of an example serving as a model.