Assessment of Stationarity Horizon of the Heart Rate

| This work presents a new method using time-varying autoregressive modelling for the assessment of heart rate signals stationarity in patients before the onset of ventricular tachyarrhythmias, including comparison with a control group. A general sta-tionarity trend is reported for all subjects, and particularly no signiicant change is observed before an arrhythmic event. Evaluation of the model tting performed by a hypothesis test suggests the presence of nonlinearities. 1 Introduction Heart rate (HR) variability analysis is a well known technique to study the interaction between the autonomic nervous system and the heart sinus pacemakers. However, classical linear methods (DFT, AR modelling) relie on the assumption of stationarity. This hypothesis is not obvious since long-term HR recordings have shown strong circadian variations, suggesting a nonstationary behaviour. Numerous studies attempted to nd out some particular features of the HR dynamics preceding the onset of ventri-cular tachyarrhythmias (VTA). However, results are still contradictory and require further investigations. The purpose of this work is to present a new method for evaluating the stationarity of the HR signal and therefore to highlight possible changes in its structure before an ar-rhythmic event. Moreover, results are compared to control subjects in upright position. The proposed method is directly derived from a para-metric approach. We consider a time-varying autoregres-sive (TVAR) model with a decomposition of the AR coef-cients variation on a set of basis functions. Stationarity is assessed by the determination of optimal orders using Rissanen's MDL criterion. Then, statistical signiicance of the TVAR coeecients is evaluated by hypothesis testing. 2 Time-Varying Autoregressive Model A discrete-time stochastic process x(n) is often expressed by an autoregressive (AR) model with p coeecients a i. When x(n) is not stationary, this approach is no longer valid, since there is no time dependence in the coeecients a i. A solution proposed by Rao 1] is to make the assumption that the variations of a i can be approximated by a linear combination of a nite number of known determi-nistic functions u k (called basis): a i (n) = P q k=0 a ik u k (n). Therefore, the TVAR model has the following form: x(n) = p X i=1 (q X k=0 a ik u k (n))x(n ? i) + (n) (1) and estimation of the coeecients a ik is performed by minimization of the mean square error. Grenier 2] and Hall & al. 3] have described with more details the identiication …