Increasing sensitivity in the measurement of heart rate variability: The method of non-stationary RR time–frequency analysis

Abstract

A novel method of the time–frequency analysis of non-stationary heart rate variability (HRV) is developed which introduces the fragmentary spectrum as a measure that brings together the frequency content, timing and duration of HRV segments. The fragmentary spectrum is calculated by the similar basis function algorithm. This numerical tool of the time to frequency and frequency to time Fourier transformations accepts both uniform and non-uniform sampling intervals, and is applicable to signal segments of arbitrary length. Once the fragmentary spectrum is calculated, the inverse transform recovers the original signal and reveals accuracy of spectral estimates. Numerical experiments show that discontinuities at the boundaries of the succession of inter-beat intervals can cause unacceptable distortions of the spectral estimates. We have developed a measure that we call the “RR deltagram” as a form of the HRV data that minimises spectral errors. The analysis of the experimental HRV data from real-life and controlled breathing conditions suggests transient oscillatory components as functionally meaningful elements of highly complex and irregular patterns of HRV.

Introduction

The variation in the timing between beats of the cardiac cycle, known as heart rate variability (HRV), has been shown to provide important insights into the balance between the two limbs of the autonomic nervous system, the sympathetic and parasympathetic branches [1]. This information has been widely used to assess the influence of the autonomic nervous system on cardiovascular control [2]. This has potential clinical significance for a variety of medical conditions, both of cardiac (myocardial infarction, congestive heart failure, life threatening arrhythmias, etc.) and non-cardiac origin (diabetes, neuropathies, obesity, etc.) [3]. Non-clinical applications include tests and monitoring of human performance under different physical and psychophysiological conditions [4]. A relatively novel field of HRV applications is the analysis of emotion regulation and psychological wellbeing, as outlined in the polyvagal theory [5].

Standard methods of HRV estimation are based on the measurement of intervals between heart beats using peaks of R waves in the electrocardiogram (ECG) as markers. One advantage of HRV based methodologies is that many of the commercial devices that are available perform automated measurement of inter-beat intervals. This means that they allow a relatively simple, non-invasive technique to be applied, thus broadening the potential range of applications for this form of measurement.

The extraction and evaluation of physiologically relevant information from HRV data is supported by both the time and frequency domain methods [6]. The conventional frequency domain measure is the power spectrum of HRV [3]. Consistently identified features of this spectrum are a low-frequency (LF) component centered around 0.1 Hz (frequency band between 0.04 and 0.15 Hz) and a high-frequency (HF) component which usually appears in the frequency band between 0.15 Hz and 0.5 Hz [3], [7]. A large body of literature suggests that HF spectrum may be a reliable marker of the vagal control of heart rate in unstressed conditions and that LF may be a marker of sympathetic activity, or combined vagal and sympathetic activity, often encountered in relatively stressful circumstances [8]. For this type of application, frequency domain measures are thought to be more selective for evaluation of the relative contributions of sympathetic and parasympathetic function in cardiac regulation than time domain parameters.

The power spectrum assumes the stationarity of data and delivers frequency domain parameters averaged over relatively long recordings of HRV. Thus, the Task Force of the European Society of Cardiology and the North American Society of Pacing Electrophysiology recommend applying spectral analysis to segments of 5-min [3]. In this context, the frequency domain parameters are regarded as measures of steady-state physiological conditions [9].

However, the steady-state measures are not suited to capture the heterogeneous properties of heart-beats. Typical aspects of non-stationarity are the presence of “patchy” patterns that change over time. The evidence of multiple pseudo-periodic and aperiodic components in such spreads of activity [10] has intensified the interest in the identification of specific patterns of HRV that may indicate dynamic aspects of the control functions of the autonomic nervous system.

The most common approach to this problem consists in the estimation of a time-dependent spectrum of HRV [11], [12]. However, the time–frequency analysis of HRV signals represents a major methodological challenge, because conventional techniques of digital spectral analysis, such as the fast Fourier transform (FFT) [13], are not suited to short-term spectral decompositions. Among novel computational tools that extend the application of classical Fourier integrals to time–frequency analysis is the similar basis function (SBF) algorithm [14]. This has the following advantages over conventional FFT:

• The transcription of the signal under analysis into a digital form accepts both uniform and non-uniform sampling intervals.

• The algorithm is applicable to signal segments of arbitrary length due to an explicit treatment of discontinuities at the boundaries of the integration intervals. This eliminates the need for windows of spectral analysis, along with their distorting impact.

In this paper we use these properties of the SBF algorithm to addresses the HRV time series as a non-stationary process. Our aim was to develop algorithms of HRV time–frequency analysis that provide a means to detect the major frequency components and measure their frequency, timing and magnitude. A simultaneous consideration of characteristic HRV patterns in both frequency and time domains is expected to provide additional insights into the mechanisms of autonomic control of heart function and may subsequently be used to discriminate between different physiological conditions in both research and clinical settings.