Ubiratan S. Freitas

Structure-selection techniques applied to continous-time nonlinear models

This paper addresses the problem of choosing the multinomials that should compose a polynomial mathematical model starting from data. The mathematical representation used is a nonlinear differential equation of the polynomial type. Some approaches that have been used in the context of discrete-time models are adapted and applied to continuous-time models. Two examples are included to illustrate the main ideas. Models obtained with and without structure selection are compared using topological analysis. The main differences between structure-selected models and complete structure models are: (i) the former are more parsimonious than the latter, (ii) a predefined fixed-point configuration can be guaranteed for the former, and (iii) the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models.

DYNAMICS UNDERLYING PATIENT-VENTILATOR INTERACTIONS DURING NOCTURNAL NONINVASIVE VENTILATION

Noninvasive ventilation is a common procedure for managing patients having chronic respiratory failure. The success of this ventilatory assistance is often linked with patients tolerance that is known to be related to the quality of the synchronization between patients spontaneous breathing cycles and ventilatory cycles delivered by the ventilator. Thirty-four sleep sessions (more than 5000 ventilatory cycles each) were automatically investigated using a specific algorithm processing airflow and pressure time series. Four groups of patients were defined according to the interplay between asynchrony events and leaks. Different mechanisms that depend on sleep stages were thus evidenced. A Shannon entropy was also proposed as a new sleep fragmentation quantification methodology.

Leakage Estimation Using Kalman Filtering in Noninvasive Mechanical Ventilation

Noninvasive mechanical ventilation is today often used to assist patient with chronic respiratory failure. One of the main reasons evoked to explain asynchrony events, discomfort, unwillingness to be treated, etc., is the occurrence of nonintentional leaks in the ventilation circuit, which are difficult to account for because they are not measured. This paper describes a solution to the problem of variable leakage estimation based on a Kalman filter driven by airflow and the pressure signals, both of which are available in the ventilation circuit. The filter was validated by showing that based on the attained leakage estimates, practically all the untriggered cycles can be explained.

Higher-Order Spectra of Nonlinear Polynomial Models for Chua's Circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chuas circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

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.

State space parsimonious reconstruction of attractor produced by an electronic oscillator

This work discusses the reconstruction, from a set of real data, of a chaotic attractor produced by a well-known electronic oscillator, Chua’s circuit. The mathematical representation used is a nonlinear differential equation of the polynomial type. One of the contributions of the present study is that structure selection techniques have been applied to help determine the regressors in the model. Models of the chaotic attractor obtained with and without structure selection were compared. The main differences between structure-selected models and complete structure models are: i) the former are more parsimonious that the latter, ii) fixed-point symmetry is guaranteed for the former, iii) for structure-selected models a trivial fixed point is also guaranteed, and iv) the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models.