Berger et al. (18) discuss various approaches for converting the sequence of RR Intervals into data suitable for subsequent frequency domain analysis. The simplest approach would be to take as the input time series the actual sequence of RR intervals. However, this Introduces a distortion in the spectrum, which intuitively corresponds to an over representation of short RR intervals and an under representation of longer RR intervals, resulting in harmonics at multiples of the fundamental frequencies. Sampling of the instantaneous RR intervals at fixed time intervals, as advocated by Berger et al., generates an unbiased time series. To avoid artifacts from the sampling process, the MIT investigators advised the use of a "boxcar" filter with a boxcar width exceeding that of the sampling interval. They found that it is reasonable to use a sampling interval of 250 to 330 milliseconds, with the instantaneous RR interval based on an interval twice the sampling interval. This approach was implemented efficiently. Mathematically, this method of sampling has the effect of convolving the heart rate signal with that of the rectangular sampling window, and this can attenuate the higher frequency power (about 5-870 at 0.40 Hz). The algorithm developed by Berger at al. at MIT accurately corrects for this frequency-dependent attenuation (18,19). The MIT time series sampling method as described by Berger at al. is used In CHRONOS.
Stationarity
The definition of stationarity comes from the theory of random processes (20). A process is wide- sense stationary if its mean is constant for all time indices (starting points), and its autocorrelatlon function depends only on lag and not on time index. Wide-sense stationarity is a requirement for much of the mathematical theory that underlies time series analysis. Since mean heart rate is almost never constant over time, tile RR interval sequence is not stationary in the mathematical sense: of course, little experimental data from any disciple could meet such stringent requirements. Nonetheless, the mean RR interval is often changing slowly with respect to the time periods under consideration (say 5 minutes). Because changes in mean RR interval are slow, it is common and often reasonable to ignore this violation. However, when analyses are to be performed on a sequence of RR interval data in which a clear trend is expected, such as that from an exercise test, investigators should consider removing trends prior to frequency domain analysis.
Methods of Spectral Analysis
Extracting periodic components from time-domain data corresponds statistically to spectral estimation. This is an enormous topic and an area of continuing active research in mathematics, statistics, and signal processing. It is also a very contentious area in which proponents of various approaches sometimes advocate their positions with great zealotry. There is no "best" method of spectral estimation.
The Fourier Transform. In "classical spectral analysis", the Fourier transform is employed to represent the time series as a sum of periodic functions. This decomposition yields a specific energy or power for a discrete set of uniformly distributed frequencies called the periodogram (21). It is necessarily true that the total power of the periodogram equals the variance of the original sequence. Thus, the Fourier transform decomposes the variance of the input data into the variance attributable to each specific frequency, analogous to the way that statistical analysis of variance - techniques divide the variance measured for a variable into that attributable to a variety of contributing factors. These techniques for estimating periodic components have been used with experimental data since the 19th century, and a rich statistical literature is available. The popularity of this sort of spectral analysis is due, in large part, to the existence of efficient mathematical algorithms for computing the Fourier transform, popularized by Cooley and Tukey (22). This fast Fourier transform or FFT is a computational technique, and not a specific means of analysis. The existence of efficient and standard computational techniques, the simple theoretical basis for the process, and the existence of a complete statistical theory for analyzing the distribution characteristics of the resulting estimates have made the discrete Fourier transform the most commonly used method for frequency domain analysis of RR interval data. The periodogram resulting from analyzing 5-minute segments of RR data has two characteristics peaks: a "low frequency'' (LF) peak near 0.10 Hz and a "high frequency" (HF) peak near 0.25 Hz. The LF peak represents both sympathetic and parasympathetic activity associated with batoreflexes and the HF peak represents respiratory modulation of RR intervals. CHRONOS uses MIT technology for computation of the RR periodogram using FFT algorithms.
