Smoothing Before Estimating Uncertainty, Scaling, and Intermittency: Application to Short Heart Rate Signals

Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence), and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the standard deviation; scaling exponents describe how dispersions change with the time scale. Intermittency has been defined as a difference between two scaling exponents. After taking a moving average, these measures give descriptive information, even for short heart rate records. For this data, dispersion and intermittency perform better than scaling exponents. 1 Electronic addresses: [email protected], [email protected]; URL: www.davidbickel.com Submitted to Fractals. 2 Introduction. Healthy and heart-failure subjects have been distinguished by various measures of heart rate variability (HRV), including measures of dispersion, scaling exponents, intermittency, and multifractality. These four classes of estimators are related: dispersion is a scale-dependent measure of uncertainty such as the standard deviation, scaling exponents specify how dispersion depends on the time scale, and intermittency and multifractality can be computed from multiple scaling exponents. One of the first estimators of HRV is the standard deviation of the heart rate; it is now wellknown that a low standard deviation is a sign of poor health. West and Goldberger [1] hypothesized that pathology would lead to a narrowing of the power spectrum of the heart rate; this would imply differences in scaling exponents between sick and healthy subjects. Such differences have been confirmed [2], but certain measures of dispersion appear to discriminate better between the two classes of subjects, especially for shorter time series [3]. For time series that are several hours long, measures of intermittency [4] and multifractality [2] also distinguish subjects with congestive heart failure from healthier subjects. However, the measurement of continuous heart rate data for such a long time is often impractical clinically since it either requires that the patients are bedridden and attached to hospital monitors, or that they wear expensive ambulatory monitors, as in Ref. 2. Many research protocols also limit the duration of monitoring: the heart rate data of Ref. [5] and of this Letter could only be collected while the nurse researchers were physically present. In addition, heart rate records that are freely available tend to be short; the public records from www.physionet.org that were