Abstract
Heart Rate Variability (HRV) data exhibit long memory and time-varying conditional variance (volatility). These characteristics are well captured using Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with Generalised AutoRegressive Conditional Heteroscedastic (GARCH) errors, which are an extension of the AR models usual in the analysis of HRV. GARCH models assume that volatility depends only on the magnitude of the shocks and not on their sign, meaning that positive and negative shocks have a symmetric effect on volatility. However, HRV recordings indicate further dependence of volatility on the lagged shocks. This work considers Exponential GARCH (EGARCH) models which assume that positive and negative shocks have an asymmetric effect (leverage effect) on the volatility, thus better copping with complex characteristics of HRV. ARFIMA-EGARCH models, combined with adaptive segmentation, are applied to 24 h HRV recordings of 30 subjects from the Noltisalis database: 10 healthy, 10 patients suffering from congestive heart failure and 10 heart transplanted patients. Overall, the results for the leverage parameter indicate that volatility responds asymmetrically to values of HRV under and over the mean. Moreover, decreased leverage parameter values for sick subjects, suggest that these models allow to discriminate between the different groups.

Abstract
This work addresses the problem of computing the time evolution of the probability density function (pdf) of the state in a nonlinear neuromuscular blockade (NMB) model, assuming that the source of uncertainty is the knowledge about one parameter. The NMB state is enlarged with the parameter, that verifies an equation given by its derivative being zero and has an initial condition described by a known pdf. By treating the resulting enlarged state-space model as a stochastic differential equation, the pdf of the state verifies a special case of the Fokker-Planck equation in which the second derivative terms vanish. This partial differential equation is solved with a numerical method based on Trotter’s formula for semigroup decomposition. The method is illustrated with results for a reduced complexity NMB model. A comparison of the predicted state pdf with clinical data for real patients is provided. © Springer International Publishing Switzerland 2014.

Abstract

Abstract
The characterization of heart rate variability (HRV) series has become important for clinical diagnosis. These series are non-stationary and exhibit long and short-range correlations. The non-parametric methodology detrended fluctuation analysis (DFA) has become widely used for the detection of these correlations. The standard procedure is to apply DFA to the RR series, estimating the desired scaling exponents. In this work we pursue an alternative approach which consists in applying DFA to the fractionally differenced RR series, Delta(RR)-R-d, where 0 < d < 1 is the long-range correlation parameter. Both methodologies are applied to 24 hour HRV series from the Noltisalis data base. We conclude that changes in HRV are better quantified by DFA scaling exponents calculated over fractionally differenced RR series than by the standard procedure. The results indicate that the scaling exponent corresponding to high frequencies obtained from Delta(RR)-R-d increases the discriminatory power among the groups: from 60% to 87% during the day period and 57% to 77% during the night period.

Abstract
This paper addresses the problem of joint estimation of the state and parameters for a deterministic continuous time system, with discrete time observations, in which the parameter vector is constant but its value is not known, being a random variable with a known distribution. Along time, the uncertainty in the parameter induces uncertainty in the plant state. The joint probability density function (pdf) satisfies the Liouville partial differential equation that is a limit case of the Fokker-Planck equation for vanishing diffusion. The continuous-discrete filter proposed operates as follows: Between two consecutive output sampling time instants, the pdf is propagated by solving the Liouville equation for an augmented state and is then corrected by using the last observation and Bayes law. An application to state estimation of the neuromuscular blockade of patients subject to general anesthesia, where parameter uncertainty is due to inter-patient variability, is described.

Abstract
This study aimed to find parameters to characterize heart rate variability (HRV) and discriminate healthy subjects and patients with heart diseases. The parameters used for discrimination characterize the different components of HRV memory (short and long) and are extracted from HRV recordings using parametric as well as non parametric methods. Thus, the parameters are: spectral components at low frequencies (LH) and high frequencies (HF) which are associated with the short memory of HRV and the long memory parameter (d) obtained from autoregressive fractionally integrated moving average (ARFIMA) models. In the non parametric context, short memory (a1) and long memory (a2) parameters are obtained from detrended fluctuation analysis (DFA). The sample used in this study contains 24-hour Holter HRV recordings of 30 subjects: 10 healthy individuals, 10 patients suffering from congestive heart failure and 10 heart transplanted patients from the Noltisalis database. It was found that short memory parameters present higher values for the healthy individuals whereas long memory parameters present higher values for the diseased individuals. Moreover, there is evidence that ARFIMA modeling allows the discrimination between the 3 groups under study, being advantageous over DFA.